An example of a conventional method of producing this type of busing is described in Japanese Laid-open Patent Publication No. 2000-218446. The method comprises the series of steps depicted in FIG. 3. First, a cylindrical body is formed in a press. The cylindrical body X, having the required height, has an intermediate base and recesses X1 and X2 at the upper and lower portions respectively. A tapered internal circumferential surface X5 is formed at one end portion of the cylindrical body X by punching the intermediate base X3 with the front end 11a of a punch 11, and, at the same time, pressing a tapered portion 11b, formed at the proximal side of the punch 11, into one end portion of the internal circumferential surface X4 of the cylindrical body X. After inverting the cylindrical body X, a tapered surface X6 is formed at the other end of the internal circumferential surface X4 by pressing another punch 12 into the cylindrical body, punch 12 having a sphere 12a at its front end, and including a tapered portion 12b. 
In the conventional production method described above, the tapered surfaces X5 and X6 are formed in sequential steps. Accordingly, as the tapered surfaces are formed, the remaining portions of the internal circumferential surface are not restrained. Consequently, displacement and deformation are liable to occur in the cylindrical body X during the formation of the tapered surfaces, and, as a result, it is difficult to make the internal circumferential surface X4 and the tapered surfaces X5 and X6 coaxial with one another. When there is a displacement between the central axis of the internal circumferential surface X4 and the central axes of the tapered surfaces X5 and X6, it is not possible to achieve accurate assembly of the bushing in a hole in an inner plate of a roller chain. This results in increased friction between the bushing and its associated pin in the roller chain. Moreover, because an accurate parallel relationship between the bushing axis and the pin axis is not maintained, the fatigue strength of the inner and outer plates is reduced.
A general object of this invention is to solve the above-described problems. More particularly, an object of the invention is to provide a method for producing a bushing, in which an accurate coaxial relationship between the internal circumferential surface of the bushing and the tapered surfaces at both end portions of the bushing is achieved, and in which the external circumferential surface of the bushing, having the required diameter, can be accurately formed.